In this paper, the control approach for a flap positioning based shape memory alloy micro-actuator is addressed. The challenge here are to model the saturation-type hysteresis in the shape memory alloy actuator, and design the controller to mitigate the effect of hysteresis and ensure the system performance. In this paper, the saturation-type hysteresis nonlinearities are represented by the generalized Prandtl-Ishlinskii model. Considering the lag effect between the temperature and the control input, the proposed robust control can stabilize the closed-loop system and ensure the accurate rotation of the flap to the desired angle without the construction of the hysteresis inverse. The effectiveness of the proposed control approach is demonstrated through a simulation example.